Figure 1: Number Line
Executive summary:
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However, in a great many textbooks and encyclopedias, one can find statements alleging that:
«There are two kinds of charge, namely positive charge and negative charge.»
That expresses what is called the two-fluid model of electric charge. The analogy to fluids supposedly works as follows:
| «There are two types of charge, namely positive charge and negative charge.» | Two types of water are available, namely hot water and cold water. |
| Combining equal amounts of positive and negative charge results in electrical neutrality. | Combining equal amounts of hot and cold water results in tepid water. |
The alternative is a one-component model of electric charge.
In reality, the charge can be represented as a point along a one-dimensional number line, as shown in figure 1. More positive charge is represented by points farther to the right on the number line, while more negative charge is represented by points farther to the left. (In contrast, if we were to take the two-fluid model seriously, we would need two variables, and the amount of so-called «charge» would be represented by a point on a two-dimensional coordinate plane, not on a one-dimensional number line.)
Note: Some people speak of a one-fluid model. That’s essentially just another name for what we are calling the one-component model. We prefer the latter name because charge isn’t exactly a fluid. It is an abstract quantity. It does, however, exhibit conservative flow in close analogy to the flow of an incompressible and indestructible fluid.
Some textbooks use the two-fluid language only in passing, using it as nothing more than a figure of speech, which isn’t so bad. However, others go out of their way to argue that the one-component model is wrong and the two-fluid model is right, which is appalling.
There has never been any good evidence in favor of a two-fluid model of electrical charge. All available evidence is consistent with the one-component model.
Note: Even in the earliest days of electrical science, back in the mid-1700s, Benjamin Franklin argued in favor of a one-fluid model. William Watson independently came to the same conclusion at about the same time.
One indispensible property of charge is its role in the law of conservation of charge. This is the starting point and the linchpin for any understanding of what “charge” means. The law of conservation of charge states that the amount of charge in a given region cannot change except by flowing across the boundary of the region. This law can be stated with great precision and formality, and has been extensively checked and confirmed. For more on what we mean by conservation, see reference 1.
Let’s see how this law applies to the following scenario: We have a closed, isolated, electrically-insulated container. Within the container there is a number Np of protons; as always, they carry one unit of positive charge apiece. There is also a number Ne of electrons; as always, they carry one unit of negative charge apiece. Finally there is a number Nn of free neutrons; they are electrically neutral. Note that neutrons that are not bound in a nucleus are unstable and undergo beta-decay with a half-life of just over 10 minutes.
If the two-fluid model were correct, we would in general need two variables to keep track of the two kinds of charge. In the previous paragraph we did use two charge-related variables (Np and Ne) but we shall soon see that this was not necessary.
Let’s make a change of variables. We define
| (1) |
The variable Q has a conventional name: it is called the charge. It can take on positive or negative values. The law of conservation of charge states that Q is conserved.1
In contrast, the law of conservation of charge says nothing about R. In fact, R has nothing to do with charge, and is not even a conserved quantity. Every time a neutron decays, R increases by two, since the decay produces a new proton and a new electron. The charge Q is conserved during this process, as it must be for any process … but R is manifestly not conserved.
Let’s be clear: we only need one variable, Q, to tell us everything we need to know about charge. Any one-variable theory can always be dressed up to look like it has two (or more) variables, but there’s no point in doing so. It would be worse than useless.
Using the two variables Q and R is mathematically equivalent to using the two variables Np and Ne. If you start with Q, that is all you will ever need to keep track of charge; you don’t need R and you don’t need to keep track of Np and Ne separately in order to keep track of the amount of charge.
Of course R is meaningful; for example, an electrically-neutral plasma (Q=0, R≫0) has much greater electrical conductivity than an electrically-neutral vacuum (Q=0, R=0). (A parallel statement can be made concerning solid state physics: A compensated semiconductor is different from an intrinsic semiconductor.) That’s all fine; it simply tells you that there’s more to physics than just charge. Still, the fact remains that the single variable Q represents the charge, and you don’t need to know anything but Q to know the charge.
Tangential remark: It turns out that the quantity B := Np + Nn is conserved in this scenario. This is not a consequence of conservation of charge; it is a consequence of another conservation law, namely conservation of baryon number. Combining conservation of B with conservation of Q, we can infer that the quantity R + 2Nn is conserved … but R by itself is not conserved.
The nature of electrical charge can be understood with even greater clarity when contrasted with the subatomic color charge: There is only one kind of electrical charge, but there are three kinds of color charge.
Terminology: The term “charge” by itself is synonymous with plain old electrical charge. If you want to refer to color charge, you have to say “color charge”.
The symmetry of color charge is described by the group SU(3), while the symmetry of electrical charge is described by the group U(1). This allows us to say with great formality and precision that there are three kinds of color charge but only one kind of electrical charge.
For more on color charge, see reference 2, reference 3, reference 4, and reference 5.
If we want to be scientific (as discussed in reference 6), due diligence requires that we examine the arguments in favor of the two-fluid model.
One argument that contains some partial truth starts from the observation that in ordinary terrestrial matter, positive charge is predominantly embodied in protons, while negative charge is predominantly embodied in electrons. This argument can be challenged on several grounds:
Charge, like other fundamental physical quantities such as energy and momentum, is something of an abstraction. The fact that it is abstract doesn’t make it any less real. (See reference 7 for a discussion of abstract things and embodiments thereof.) We don’t say that momentum embodied in a piece of wood is in any fundamental way different from momentum embodied in a piece of plastic; the embodiment is different, but the momentum is fundamentally the same. By the same token, the charge embodied in protons is fundamentally the same as the charge embodied in electrons (with due regard for signs).
It’s a mistake to overemphasize the currents and the embodiments. In a sample containing a mixture of five acids, there will be six different kinds of current. That alone should suffice to invalidate all the arguments in favor of a two-fluid model; if you’re going to allow more than one, logic requires you to allow an unlimited number.
The smart way to proceed is to say that there is only one kind of charge, just as there is only one kind of momentum. The momentum is the same kind of momentum, no matter whether it is embodied in electrons, protons, wood, plastic, or whatever. By the same token, the charge is the same kind of charge, no matter whether it is embodied in electrons, protons, ions, subatomic particles, or whatever.
Charge is not matter, and matter is not charge. If you mean “charge”, you should say “charge”, while if you mean “charged particle”, you should say “charged particle”. There exist many kinds of charged particles, but only one kind of electrical charge.
It would be particulary unwise to mention the two-fluid model in an introductory course.
Such courses often explore the topic of electricity by means of simple macroscopic experiments. These may include rubbing a rubber rod on fur, peeling bits of cellophane tape off the desktop, and testing for the presence of charge using home-made electroscopes.
Macroscopic experiments of this sort do not provide any evidence whatsoever for preferring the two-fluid model to the one-component model. Even the fallacious arguments mentioned in section 3 are inapplicable in such a situation, because they involve microscopic issues that are not addressed by the introductory-level macroscopic experiments.
If we restrict attention to this sort of simple macroscopic experiments and nothing else, the two-fluid model and the one-component model are both equally-viable hypotheses. However, there is more to physics than simple experiments; there is also theory, and there are more advanced experiments. There are at least three ways to discriminate between the two-fluid model and the one-component model:
In an introductory class, there is no need to emphasize the one-component theory, nor to refute the two-fluid theory, nor even to mention the two-fluid theory (unless a student brings it up). The sensible approach is just to introduce the idea of “charge”, say that the amount of charge Q can be positive, zero, or negative, and proceed from there. This is the approach taken by some textbooks (e.g. reference 8). There is no need to make things more complicated than that. The simple and obvious answer is the fundamentally correct answer.